Download Downward Nominal Wage Rigidity, Currency Pegs, and Involuntary

Downward Nominal Wage Rigidity, Currency
Pegs, and Involuntary Unemployment
Stephanie Schmitt-Grohé
Columbia University, Centre for Economic Policy Research, and National Bureau of Economic Research
Martı́n Uribe
Columbia University and National Bureau of Economic Research
This paper analyzes the inefficiencies arising from the combination
of fixed exchange rates, nominal rigidity, and free capital mobility. We
document that nominal wages are downwardly rigid in emerging countries. We develop an open-economy model that incorporates this friction. The model predicts that the combination of a currency peg and
free capital mobility creates a negative externality that causes overborrowing during booms and high unemployment during contractions.
Optimal capital controls are shown to be prudential. For plausible calibrations, they reduce unemployment by around 5 percentage points.
The optimal exchange rate policy eliminates unemployment and calls
for large devaluations during crises.
I. Introduction
The combination of a fixed exchange rate and free capital mobility can be
a mixed blessing. A case in point is the European currency union. Figure 1
This paper merges two earlier papers: “Pegs and Pain” and “Prudential Policy for Peggers”
(Schmitt-Grohé and Uribe 2010, 2012). We thank Gianluca Benigno, Javier Bianchi, Ester
Faia, Philip Harms, Olivier Jeanne, Robert Kollmann, Anna Kormilitsina, José L. Maia, Juan
Pablo Nicolini, Chris Otrok, Jaume Ventura, Harald Uhlig (the editor), three anonymous
referees, and seminar participants at numerous institutions for comments; Ozge Akinci,
Ryan Chahrour, Stephane Dupraz, and Pablo Ottonello for excellent research assistance;
and the National Science Foundation for research support.
Electronically published August 30, 2016
[ Journal of Political Economy, 2016, vol. 124, no. 5]
© 2016 by The University of Chicago. All rights reserved. 0022-3808/2016/12405-0003$10.00
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F IG . 1.—Boom-bust cycle in peripheral Europe: 2000–2011. Data Source: Eurostat. Sample period, 2000:Q4–2011:Q3. Data represent arithmetic mean
of Bulgaria, Cyprus, Estonia, Greece, Ireland, Lithuania, Latvia, Portugal, Spain, Slovenia, and Slovakia. The vertical dotted line indicates 2008:Q2, the
onset of the Great Contraction in Europe. Detailed data sources and country-by-country plots are available in online appendix A. The data are provided
with the online materials of this paper. Color version available as an online enhancement.
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journal of political economy
displays the average current-account-to-GDP ratio, an index of nominal
hourly wages in euros, and the rate of unemployment for a group of peripheral European countries that were either on or pegging to the euro
over the period 2000–2011. In the early 2000s, these countries enjoyed large
capital inflows, which, through their expansionary effect on domestic absorption, led to sizable appreciations in hourly wages. With the onset of
the global recession in 2008, capital inflows dried up and aggregate demand collapsed. At the same time, nominal wages remained at the level
they had achieved at the peak of the boom. The combination of depressed
levels of aggregate demand and high nominal wages was associated with a
massive increase in involuntary unemployment. In turn, local monetary
authorities were unable to reduce real wages via a devaluation because
of their commitment to the currency union.
This narrative evokes several interrelated questions. What is the optimal exchange rate policy in an open economy with downward nominal
wage rigidity? What are the welfare costs of currency pegs vis-à-vis the optimal exchange rate policy in the presence of downward nominal wage
rigidity? Can fixed exchange rate regimes benefit from imposing capital
controls? If so, are optimal capital controls prudential in nature; that is,
is it optimal to tax capital inflows during booms and subsidize them during contractions? How large are the welfare gains of optimal capital controls for peggers?
In this paper, we address these five questions both analytically and
quantitatively. To this end, we develop a model of an open economy with
downward nominal wage rigidity. The motivation for focusing on downward nominal wage rigidity is empirical. There exists a large literature suggesting that downward nominal wage rigidity is pervasive in developed
countries. In this paper, we provide new evidence suggesting that this is
also the case among emerging-market economies.
The model predicts an endogenous connection between macroeconomic volatility and the mean level of unemployment. This connection
is due to the nature of the assumed labor contract, according to which employment is demand determined during contractions but supply and demand determined during booms. As a result, involuntary unemployment
emerges during downturns and full employment during booms. Consequently, aggregate fluctuations cause unemployment on average. Importantly, the average level of unemployment is increasing in the amplitude
of the business cycle, opening the door to large welfare gains from macroeconomic stabilization policy.
The paper establishes that the combination of downward nominal wage
rigidity, a fixed exchange rate, and free capital mobility creates a negative externality. The externality causes overborrowing during booms and
excessive unemployment during contractions. The nature of the external-
downward nominal wage rigidity
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ity is that expansions in aggregate demand drive up wages, putting the
economy in a vulnerable situation. For in the contractionary phase of
the cycle, downward nominal wage rigidity and a fixed exchange rate prevent real wages from falling to the level consistent with full employment.
Agents understand this mechanism but are too small to internalize the fact
that their individual expenditure decisions collectively cause inefficiently
large increases in wages during expansions.
The existence of the externality creates a rationale for government intervention. We consider two types of policy intervention. First, we study
interventions that achieve the first-best allocation. We show that the firstbest allocation can be brought about either via exchange rate policy or
via labor or production subsidies at the level of the firm financed by income taxes levied at the level of the household.
The optimal exchange rate policy consists in engineering large devaluations of the domestic currency during contractions. The purpose of these
devaluations is to reduce the real value of wages. Importantly, these optimal devaluations are not of the beggar-thy-neighbor type because they
do not aim to foster exports by altering the terms of trade. Rather, they
are geared toward correcting the distortion in the labor market created
by downward nominal wage rigidity. Versions of the model calibrated to
emerging-country data predict that boom-bust episodes like the ones that
took place in Argentina in 2001 or in peripheral Europe in 2008, in which
output falls by two standard deviations from peak to trough over a time
span of 10 quarters, call for devaluations of about 100 percent.
The second type of policy intervention we consider is one in which the
policy maker is constrained to stick to a currency peg and faces limitations to change domestic fiscal policy. Instead, he resorts to imposing capital controls. We show that in fixed exchange rate economies the Ramseyoptimal capital control tax is prudential in nature, as it restricts capital
inflows in good times and subsidizes external borrowing in bad times.
The benevolent government has an incentive to levy taxes on external
debt during expansions as a way to limit nominal wage growth. Moderating wage growth during booms helps ameliorate the unemployment
problem caused by downward wage rigidity during subsequent contractions. We show that the government determines the optimal capital control policy as the solution to a trade-off between intertemporal distortions
caused by the capital controls themselves and static distortions caused
by the combination of downward nominal wage rigidity and a fixed exchange rate.
Quantitative analysis based on a plausible calibration of the model to
emerging-country data suggests that currency pegs coupled with free capital mobility lead to high average levels of unemployment of more than
8 percent. In turn, large levels of unemployment translate into large wel-
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fare losses. Capital controls are shown to be highly effective at curbing
overborrowing during booms and reducing unemployment during busts.
In the baseline calibration, optimal capital controls reduce the average
rate of unemployment from over 8 percent to below 3 percent. This means
that the trade-off faced by the policy maker between alleviating the static
distortions in the labor markets and interfering with the efficient intertemporal allocation of tradable absorption through capital controls is resolved largely in favor of the former.
This paper is related to the Mundellian literature on the trilemma of
international finance, according to which a country cannot have at the
same time a fixed exchange rate, free capital mobility, and an independent interest rate policy. A number of studies have analyzed the welfare
consequences of currency pegs in the context of models with nominal
rigidities (e.g., Kollmann 2002; Galí and Monacelli 2005). There is also
a body of work on the role of capital controls as a stabilization instrument.
A strand of this literature stresses financial distortions, such as collateral
constraints on external borrowing as a rationale for capital controls (Auernheimer and García-Saltos 2000; Uribe 2006, 2007; Lorenzoni 2008;
Caballero and Lorenzoni 2009; Korinek 2010; Benigno et al. 2011; Bianchi
2011; Bianchi and Mendoza 2012; Jeanne and Korinek 2013). Another
line of work is based on the classical trade theoretic argument that governments of large countries have incentives to apply capital controls as
a means to induce households to internalize the country’s market power
in financial markets (e.g., Obstfeld and Rogoff 1996; Costinot, Lorenzoni,
and Werning 2011). Our theory of capital controls is distinct from the
above two in that it does not assume the existence of collateral constraints
or market power in financial markets. In a recent related paper, Farhi
and Werning (2012) study capital controls in the context of a perfectforesight, linearized version of the Galí and Monacelli (2005) sticky-price
model.
The remainder of the paper is organized as follows. Section II develops
the theoretical model. Section III identifies the negative externality arising from the combination of downward nominal wage rigidity, fixed exchange rates, and free capital mobility. Sections IV, V, and VI characterize
equilibrium dynamics under optimal exchange rate policy, optimal fiscal
policy under a currency peg, and optimal capital control policy under a
currency peg, respectively. Section VII shows by means of an analytical example that optimal capital controls are prudential. Section VIII presents empirical evidence on downward nominal wage rigidity in emerging countries. Section IX analyzes quantitatively the adjustment of the economy to
a boom-bust cycle under the various policy arrangements described above.
It also contains the main quantitative results on the effects of the aforementioned policy interventions on overborrowing, average unemployment,
and welfare. Section X presents conclusions.
downward nominal wage rigidity
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II. An Open Economy with Downward Nominal Wage Rigidity
We develop a model of a small open economy in which nominal wages
are downwardly rigid. The model features two types of goods, tradables
and nontradables. The economy is driven by two exogenous shocks, a
country–interest rate shock and a terms-of-trade shock.
A.
Households
The economy is populated by a large number of identical households
with preferences described by the utility function
∞
E0 obt U ðct Þ,
(1)
t50
where ct denotes consumption, U is a strictly increasing and concave period utility function, and b ∈ (0, 1) is the subjective discount factor. The
symbol Et denotes the mathematical expectations operator conditional
on information available in period t. The consumption good is a composite of tradable consumption, ctT , and nontradable consumption, ctN .
The aggregation technology has the form
ct 5 AðctT , ctN Þ,
(2)
where A(, ) is an increasing, concave, and linearly homogeneous function.
We assume full liability dollarization. Specifically, households have access to a one-period, internationally traded, state-noncontingent bond denominated in tradables. We let dt denote the level of debt assumed in period t 2 1 and due in period t and rt the interest rate on debt held between
periods t and t 1 1. The sequential budget constraint of the household is
given by
PtT ctT 1 PtN ctN 1 Et dt 5 PtT ytT 1 Wt ht 1 Ft 1
Et dt11
,
1 1 rt
(3)
where PtT denotes the nominal price of tradable goods, PtN the nominal
price of nontradable goods, Et the nominal exchange rate defined as the
domestic currency price of one unit of foreign currency, ytT the endowment of traded goods, Wt the nominal wage rate, ht hours worked, and
Ft nominal profits from the ownership of firms. The variables rt and ytT
are assumed to be exogenous and stochastic. Movements in ytT can be interpreted either as shocks to the physical availability of tradable goods or
as shocks to the country’s terms of trade.
Households supply inelastically h hours to the labor market each period. The assumption of an inelastic labor supply is motivated in part by
microeconometric evidence (e.g., Blundell and MaCurdy 1999) and mac-
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roeconometric evidence from models with nominal rigidities (e.g., Smets
and Wouters 2007; Justiniano, Primiceri, and Tambalotti 2010) suggesting
that the labor supply elasticity is near zero. A second reason for assuming
an inelastic labor supply is that it makes the workings of our two-sector
model more transparent. In section G.5 of the online appendix, we relax
this assumption by endogenizing the labor supply decision. Because of the
presence of downward nominal wage rigidity, households may not be able
to sell all of the hours they supply. As a result, households take employ as exogenously given.
ment, ht ≤ h,
Households are assumed to be subject to the following debt limit, which
prevents them from engaging in Ponzi schemes:
dt11 ≤ d,
(4)
where d denotes the natural debt limit.
We assume that the law of one price holds for tradables. Specifically, letT
ting Pt * denote the foreign currency price of tradables, the law of one price
T
implies that PtT 5 Pt * Et : We further assume that the foreign currency
T
price of tradables is constant and normalized to unity, Pt * 5 1. In the
quantitative analysis, we relax this assumption. Thus, we have that the
nominal price of tradables equals the nominal exchange rate, PtT 5 Et :
Households choose contingent plans fct , ctT , ctN , dt11 g to maximize (1)
subject to (2)–(4) taking as given PtT , PtN , Et, Wt, ht, Ft, rt, and ytT . Letting
pt ;
PtN
PtT
denote the relative price of nontradables in terms of tradables and using
the fact that PtT 5 Et , the optimality conditions associated with this problem are (2)–(4) and
A2 ðctT , ctN Þ
5 pt ,
A1 ðctT , ctN Þ
(5)
lt 5 U 0 ðct ÞA1 ðctT , ctN Þ,
lt
5 bEt lt11 1 mt ,
1 1 rt
(6)
mt ≥ 0,
mt ðdt11 2 dÞ 5 0,
where lt =PtT and mt denote the Lagrange multipliers associated with (3)
and (4), respectively.
downward nominal wage rigidity
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F IG . 2.—Demand and supply schedules of nontradable goods
Equation (5) describes the demand for nontradables as a function of the
relative price of nontradables, pt, and the level of tradable absorption, ctT.
Given ctT , the demand for nontradables is strictly decreasing in pt. This is a
consequence of the assumptions made about the aggregator function A.
It reflects the fact that as the relative price of nontradables increases, households tend to consume relatively less nontradables. The demand function
for nontradables is depicted in the left panel of figure 2 with a downwardsloping solid line. An increase in the absorption of tradables shifts the demand schedule up and to the right, reflecting normality. Such a shift is
shown with a dashed downward-sloping line in the left panel of figure 2
for an increase in traded consumption from c0T to c1T > c0T. Absorption of
tradables can be viewed as a shifter of the demand for nontradables. Of
course, ctT is itself an endogenous variable, which is determined simultaneously with all other endogenous variables of the model.
B. Firms
Nontraded output, denoted ytN , is produced by perfectly competitive
firms. Each firm operates a production technology given by ytN 5 F ðht Þ,
which uses labor services as the sole input. The function F is assumed to
be strictly increasing and strictly concave. Firms choose the amount of labor input to maximize profits, given by Ft ; PtN F ðht Þ 2 Wt ht : The optimality condition associated with this problem is PtN F 0 ðht Þ 5 Wt : Dividing
both sides by PtT and using the facts that PtT 5 Et and ht 5 F 21 ðytN Þ yields
a supply schedule of nontradable goods of the form
pt 5
Wt =Et
:
F ðF 21 ðytN ÞÞ
0
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This supply schedule is depicted with a solid upward-sloping line in the
right panel of figure 2. Ceteris paribus, the higher the relative price of
the nontraded good, the larger the supply of nontradable goods. Also,
all other things equal, the higher the labor cost, Wt =Et , the smaller the
supply of nontradables at each level of the relative price pt. That is, an increase in the nominal wage rate, holding constant the nominal exchange
rate, causes the supply schedule to shift up and to the left. The right panel
of figure 2 displays with a broken upward-sloping line the shift in the supply schedule that results from an increase in the nominal wage rate from
W0 to W1 > W0, holding the nominal exchange rate constant at E0. Similarly, a currency devaluation, holding the nominal wage constant, shifts
the supply schedule down and to the right (not shown). Intuitively, a devaluation that is not accompanied by a change in nominal wages reduces
the real labor cost, thereby inducing firms to increase the supply of nontradable goods for any given relative price.
C. Downward Nominal Wage Rigidity
The central friction in the model is downward nominal wage rigidity.
Specifically, we impose that
Wt ≥ gWt21 , g > 0:
(7)
The parameter g governs the degree of downward nominal wage rigidity.
The higher g is, the more downwardly rigid nominal wages are. This setup nests the cases of absolute downward rigidity when g ≥ 1 and full wage
flexibility when g 5 0. In Section VIII, we present empirical evidence suggesting that g is close to unity in low-inflation emerging economies.
The presence of downwardly rigid nominal wages implies that the labor
market will in general not clear. Instead, involuntary unemployment, given
by h 2 ht , will be a regular feature of this economy. Actual employment
must satisfy
ht ≤ h
(8)
at all times. At any point in time, wages and employment must satisfy the
slackness condition
ðh 2 ht ÞðWt 2 gWt21 Þ 5 0:
(9)
must be acThis condition states that periods of unemployment (ht < h)
companied by a binding wage constraint. It also states that when the wage
constraint is not binding (Wt > gWt21 ), the economy must be in full em
ployment (ht 5 h).
We note that the assumed structure of the labor market is perfectly competitive. Both workers and employers are wage takers. Alternatively, one
downward nominal wage rigidity
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could assume market power on either side. In the related new Keynesian
literature, it is customary to assume that workers have market power and
set wages to maximize their lifetime utility. As emphasized by Elsby (2009),
in the presence of a lower bound on nominal wages, this market structure
might give rise to an endogenous compression of wage increases in anticipation of future adverse shocks. The empirical evidence, however, suggests that strategic wage compression may have played a relatively minor
role in recent boom-bust episodes. For instance, as documented in figure 1, nominal hourly wages in the periphery of the euro zone increased
over 60 percent during the boom of 2000–2008 in spite of low inflation
and virtually no growth in total factor productivity.1
D. Equilibrium
In equilibrium, the market for nontraded goods must clear at all times.
That is, the condition
ctN 5 ytN
must hold for all t. Combining this condition, the production technology for nontradables, the household’s budget constraint, and the definition of firms’ profits, we obtain the market-clearing condition for traded
goods,
ctT 1 dt 5 ytT 1
dt11
:
1 1 rt
Letting wt ; Wt =Et denote the real wage in terms of tradables and
et ;
Et
Et21
the gross rate of devaluation of the domestic currency, we define an equilibrium as follows.
Definition 1 (Equilibrium). An equilibrium is a set of stochastic processes fctT , ht , wt , dt11 , lt , mt g∞t50 satisfying
ctT 1 dt 5 ytT 1
dt11 ≤ d,
dt11
,
1 1 rt
(10)
(11)
1
Barkbu, Rahman, and Valdés (2012) show that for the euro area as a whole, total factor
productivity grew by less than 0.2 percent per year between 2000 and 2010. Productivity
growth in the periphery of Europe was even weaker. According to data from the EU Klems
Growth and Productivity Account Project, between 2000 and 2007, value-added total factor
productivity fell by 4 percent in Spain and by 1 percent in Ireland.
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journal of political economy
mt ≥ 0,
(12)
mt ðdt11 2 d Þ 5 0,
(13)
lt 5 U 0 ðAðctT , F ðht ÞÞÞA1 ðctT , F ðht ÞÞ,
(14)
lt
5 bEt lt11 1 mt ,
1 1 rt
(15)
A2 ðctT , F ðht ÞÞ
w
5 0 t ,
T
A1 ðct , F ðht ÞÞ F ðht Þ
(16)
wt ≥ g
wt21
,
et
(17)
ht ≤ h,
(18)
wt21
5 0,
ðht 2 hÞ wt 2 g
et
(19)
given an exchange rate policy, fet g∞t50 , initial conditions w21 and d0, and
exogenous stochastic processes frt , ytT g∞t50 .
We characterize analytically equilibrium under four alternative policy
regimes: a currency peg with free capital mobility, the optimal exchange
rate policy, optimal fiscal policy under currency pegs, and optimal capital controls under currency pegs.
III. Currency Pegs with Free Capital Mobility
A currency peg is an exchange rate policy in which the nominal exchange
rate is fixed. The gross devaluation rate therefore satisfies
et 5 1,
(20)
for t ≥ 0. Under a currency peg, the economy is subject to two nominal
rigidities. One is policy induced: The nominal exchange rate, Et, is kept
fixed by the monetary authority. The second is structural and is given by
the downward rigidity of the nominal wage Wt. The combination of these
two nominal rigidities results in a real rigidity. Specifically, the real wage,
wt, is downwardly rigid and, when falling, moves sluggishly at a rate no
larger than 1 2 g. The labor market is therefore, in general, in disequilibrium and features involuntary unemployment. Unemployment is a function of the amount by which the past real wage exceeds the current fullemployment real wage. It follows that under a currency peg, the past real
wage, wt21, becomes a relevant state variable for the economy.
downward nominal wage rigidity
A.
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A Peg-Induced Externality
The combination of downward nominal wage rigidity and a currency peg
creates a negative externality. The nature of this externality is that in periods of economic expansion, elevated demand for nontradables drives
nominal (and real) wages up placing the economy in a vulnerable situation. For in the contractionary phase of the cycle, downward nominal
wage rigidity and the currency peg hinder the downward adjustment of
real wages, causing unemployment. Individual agents understand this
mechanism but are too small to internalize the fact that their own expenditure choices collectively exacerbate disruptions in the labor market.
Figure 3 illustrates the peg-induced externality by considering the adjustment of the economy to a boom-bust episode. Because in equilibrium ctN 5 ytN 5 F ðht Þ, the figure plots the demand and supply schedules
for nontraded goods in terms of employment in the nontraded sector, so
that the horizontal axis measures ht. The intersection of the demand and
supply schedules, therefore, indicates the equilibrium demand for labor,
given ctT and Wt =Et . The figure also shows with a dotted vertical line the
F IG . 3.—Adjustment to a boom-bust episode under a currency peg. The figure is drawn
under the assumption that g 5 1.
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journal of political economy
Suppose that the initial position of the economy is at point
labor supply, h.
SupA, where the labor market is operating at full employment, ht 5 h.
pose that in response to a positive external shock, such as a decline in
the country interest rate, traded absorption increases from c0T to c1T >
c0T , causing the demand function to shift up and to the right. If nominal
wages stayed unchanged, the new intersection of the demand and supply
schedules would occur at point B. However, at point B the demand for la The excess demand for
bor would exceed the available supply of labor h.
labor drives up the nominal wage from W0 to W1 > W0 , causing the supply
schedule to shift up and to the left. The new intersection of the demand
and supply schedules occurs at point C, where full employment is restored and the excess demand for labor has disappeared. The transition
from points A to C happens instantaneously because nominal wages are
upwardly flexible. Although the economy is enjoying full employment,
the increase in nominal wages is a harbinger of bad things to come.
Suppose now that the positive external shock fades away and that, as
a consequence, absorption of tradables goes back to its normal level c0T .
The decline in ctT shifts the demand schedule back to its original position,
indicated by the downward-sloping solid line. However, the economy does
not return to point A. Because of downward nominal wage rigidity, the nominal wage stays at W1, and because of the currency peg, the nominal exchange rate remains at E0. As a result, the supply schedule continues to
be the broken upward-sloping line. The new intersection is at point D.
There, the economy suffers involuntary unemployment equal to h 2 h bust .
If individual households could internalize the fact that consumption booms
lead to excessive wage growth and unemployment once the boom is over,
they might choose to restrain their appetite for tradable goods during the
boom. This is the precise nature of the peg-induced externality.
B. Volatility and Mean Unemployment
The present model implies an endogenous connection between the amplitude of the cycle and the average levels of involuntary unemployment
and output. This connection opens the door to large welfare gains from
optimal stabilization policy and is rooted in the fact that under a currency
peg the economy adjusts asymmetrically to positive and negative external
shocks. The adjustment to positive external shocks is efficient, as nominal wages adjust upward to ensure that firms are on their labor demand
schedule and households on their labor supply schedule. In sharp contrast, the adjustment to negative external shocks is inefficient, as nominal
wages fail to fall, forcing households off their labor supply schedule and
generating involuntary unemployment. It follows that over the business
cycle, the model economy fluctuates between periods of full employment
and an efficient level of production and periods of involuntary unem-
downward nominal wage rigidity
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ployment and inefficiently low levels of production. Therefore, the average levels of involuntary unemployment and nontraded output depend
on the amplitude of the business cycle. That is, in this model, mean unemployment is increasing in the variance of the underlying shocks. This
property of the model obtains even if wage rigidity is symmetric (i.e., even
if nominal wages are equally rigid upwardly and downwardly). The reason
is that in the present model employment is determined by the smaller of
demand and supply, as opposed to demand alone, as is the case in existing sticky-wage models in the Erceg, Henderson, and Levin (2000) and
Galí (2011) tradition. Asymmetric wage rigidity exacerbates the connection between the volatility of the underlying shocks and the average level
of involuntary unemployment.
IV.
Optimal Exchange Rate Policy
Consider an exchange rate policy in which the central bank always sets
the devaluation rate to ensure full employment in the labor market, that
for all t ≥ 0. We refer to this exchange rate aris, to ensure that ht 5 h,
rangement as the full-employment exchange rate policy and will show
that it supports the Pareto-optimal allocation. The equilibrium dynamics
associated with the full-employment exchange rate policy are illustrated
in figure 3. Suppose that, after being hit by a negative external shock, the
economy is stuck at point D with involuntary unemployment equal to
h 2 h bust . At point D, the desired demand for tradables is c0T , the nominal
wage is W1, and the nominal exchange rate is E0. Suppose that the central
bank were to devalue the domestic currency so as to deflate the purchasing power of nominal wages to a point consistent with full employment.
That is, suppose that the central bank sets the exchange rate at the level
E1 > E0 satisfying
T
5 A2 ðc0T , F ðhÞÞ=A
ðW1 =E1 Þ=F 0 ðhÞ
1 ðc0 , F ðhÞÞ:
In this case the supply schedule would shift down and to the right, intersecting the demand schedule at point A, where unemployment is nil
Under the full-employment exchange rate policy, the relative
(h 5 h).
price of nontradables falls from p boom at the peak of the cycle to p0 after
the negative external shock. By contrast, if the central bank had kept the
exchange rate fixed, the relative price of nontradables would have fallen
by less, namely, from p boom to p bust. The reason why in the currency peg
economy firms are reluctant to implement sufficiently large price cuts
is that real wages, and therefore labor costs, remain as high as they were
during the boom. By contrast, the devaluation lowers the real cost of labor, making it viable for firms to slash prices. In turn, because under the
peg prices remain high, households do not receive a strong enough sig-
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journal of political economy
nal to switch expenditures away from tradables and toward nontradables
in a magnitude compatible with full employment.
The full-employment policy amounts to setting the devaluation rate to
ensure that the real wage equals the full-employment real wage. We denote the full-employment real wage by qðctT Þ, where the function qðctT Þ is
given by
qðctT Þ ;
A2 ðctT , F ðhÞÞ
0 T
F ðhÞ:
A1 ðct , F ðhÞÞ
(21)
The assumed properties of the aggregator function A ensure that the
function qðÞ is strictly increasing in ctT .
The full-employment exchange rate policy stipulates that should the
nominal value of the full-employment real wage evaluated at last period’s
nominal exchange rate, qðctT ÞEt21 , fall below the lower bound gWt21 , then
the central bank devalues the domestic currency to ensure that qðctT ÞEt ≥
gWt21 . That is, the devaluation rate makes the nominal wage, Wt, greater
than or equal to its lower bound, gWt21 , and at the same time guarantees
that the real wage, wt, equals the full-employment real wage qðctT Þ. In general, any exchange rate policy satisfying
et ≥ g
wt21
qðctT Þ
(22)
ensures full employment at all times. All exchange rate policies pertaining to this family deliver the same real allocation and are therefore equivalent from a welfare point of view. Indeed, the real allocation induced by
policies belonging to this family is Pareto optimal. The following proposition establishes these results.
Proposition 1. Any exchange rate policy satisfying condition (22) is
consistent with a real allocation that exhibits full employment (ht 5 h)
at all dates and states and is Pareto optimal.
Proof. See online appendix B.
o
g∞t50 , is the solution to
The Pareto-optimal allocation, denoted fctTo , dt11
the following value function problem:
T
1 bEt v o ðyt11
, rt11 , dt11 Þg
v o ðytT , rt , dt Þ 5 max fU ðAðctT , F ðhÞÞÞ
fctT ,dt11 g
(23)
subject to (10) and (11), where the function v o ðytT , rt , dt Þ represents the
welfare level of the representative agent in state ðytT , rt , dt Þ. The facts that
under the optimal exchange rate policy aggregate dynamics can be described as the solution to a Bellman equation and that the past real wage,
wt21, is not a relevant state variable in period t greatly facilitate the quantitative characterization of the model’s predictions.
downward nominal wage rigidity
1481
V. Optimal Fiscal Policy under a Currency Peg
and Free Capital Mobility
Many observers have suggested the use of fiscal policy to ease the pains
of currency pegs. However, advocates of active fiscal policy do not speak
with a single voice. Some argue that the right medicine is fiscal restraint
via tax increases and cuts in public expenditures. Others hold diametrically opposed views and argue that only widespread increases in government spending and tax cuts can offer pain relief. Our model suggests
that both of these extreme views are misguided. Instead, the model suggests that the way to ease the pain of a currency peg by means of fiscal
policy is more sophisticated in nature. In particular, optimal fiscal policy
in the context of a currency peg can be implemented by a time-varying
wage subsidy at the firm level, financed with income taxes at the household level.
Suppose that the exchange rate is pegged (et 5 1) and that the government subsidizes employment at the firm level at the rate tht and levies iny
come taxes at the household level at the rate tt . The sequential budget
constraint of the household is then given by
ctT 1 pt ctN 1 dt 5 ð1 2 tyt ÞðytT 1 wt ht 1 ft Þ 1
dt11
,
1 1 rt
(24)
where ft ; Ft =Et denotes real profits in terms of tradables. Note that
y
the proportional income tax tt is nondistorting, because households
T
take yt , wt ht , and ft as given. Consequently, the first-order conditions
of the household are as in the economy without income taxes (see
Sec. II.A).
With the wage subsidy, profits of firms expressed in terms of tradables
are given by ft 5 pt F ðht Þ 2 ð1 2 tht Þwt ht . The optimality condition for
profit maximization is
pt 5
ð1 2 tht Þwt
:
F 0 ðht Þ
(25)
We assume that the government consumes no goods, starts with no
debt, and maintains a balanced budget period by period. Thus, its sequential budget constraint is given by
tht wt ht 5 tyt ðytT 1 wt ht 1 ft Þ :
(26)
All other aspects of the model are as in the currency peg economy without taxes.
The Pareto-optimal equilibrium can be supported under a currency
peg by setting the payroll subsidy tht as
1482
journal of political economy
qðctT Þ
:
(27)
tht 5 max 0, 1 2
gwt21
The following proposition establishes this result.
Proposition 2 (Optimal wage subsidy under a currency peg). Suppose that the exchange rate policy is characterized by a currency peg.
Then, the labor subsidy given in equation (27) supports the Paretooptimal allocation.
Proof. See online appendix C.
The intuition why a wage subsidy can implement the Pareto-optimal
allocation is straightforward and is closely linked to how the optimal devaluation policy works. Equation (25) is the supply schedule of nontradables plotted in figure 3, with the after-subsidy real wage ð1 2 tht Þwt replacing Wt =Et . Increases in tht shift this schedule down and to the right,
just as devaluations do. In particular, when the economy is stuck at a
point like D in the figure, with involuntary unemployment given by h 2
hbust , the government can induce a shift of the supply schedule down and
to the right by increasing the labor subsidy tht , which reduces the labor
cost perceived by firms. If the increase in the labor subsidy is of the right
size, the equilibrium will be at point A, where full employment is restored. In this way, the fiscal authority can fully offset the real rigidity created by the combination of downward nominal wage rigidity and a currency peg.
It is straightforward to show that the Pareto-optimal allocation can
also be brought about via consumption or sale subsidies in the nontraded sector at the same rate tht characterized in the above proposition.2
Also, we assumed that the wage subsidy given in equation (27) is financed by a uniform income tax. However, it can be shown that the subsidy scheme can also be financed by an appropriate proportional tax
on any individual source of income (labor income, wt ht , tradable income, ytT , profits, ft) or any combination thereof. Furthermore, these financing schemes work even when the labor supply is elastic. The reason
is that the subsidy is positive only in states of the world in which, in the
absence of the subsidy, households are off their labor supply schedule,
or involuntarily unemployed.
It is clear from equation (27) that the optimal subsidy inherits the stochastic properties of the optimal devaluation rate studied in previous
sections (see eq. [22]). Because, as we will see shortly, under plausible
calibrations the optimal devaluation rate is found to be highly volatile
at business cycle frequency, it follows that the fiscal alternative presented
here may indeed introduce an impractically high level of volatility in labor subsidy or labor tax rates.
2
In a more recent contribution, Farhi, Gopinath, and Itskhoki (2011) expand this idea
to other economic environments.
downward nominal wage rigidity
VI.
1483
Optimal Capital Controls under a Currency Peg
In Section III.A, we established that the combination of a currency peg
and downward nominal wage rigidity creates an externality. During episodes of large capital inflows, nominal wages rise, making the economy
vulnerable to unemployment once capital inflows dry up, as nominal
wages cannot adjust downwardly to equilibrate the labor market. Individuals understand this source of fragility but are too small to do anything
about it. Thus, under a currency peg and free capital mobility, the economy overborrows during booms and suffers excessive unemployment
during contractions. Consequently, the government has an incentive to
intervene.
In this section, we study the efficacy of capital controls in remedying
the peg-induced externality. We interpret the concept of capital controls
broadly, as regulations of cross-border financial flows. For instance, the
set of financial reform measures developed by the Basel Committee on
Banking Supervision, known as Basel III, contemplates the use of procyclical capital requirements for banks. This type of regulation is of interest because it tends to act like capital controls but without violating
possible arrangements governing flows of financial capital across borders, like those existing in the European Union.
Specifically, we explore the possibility that the government acts prudentially by imposing capital controls during booms. Such a policy
would tend to curb capital inflows and in that way contain the rise in
nominal wages and limit the size of involuntary unemployment once
the boom is over. Our approach is not to assume that capital controls
are prudential, but rather to investigate whether prudential capital control policy emerges endogenously as a Ramsey-optimal outcome.
The intuition for why the government may wish to use capital controls
in a prudential manner is illustrated in figure 4. Suppose that the economy starts at point A. At that point traded consumption is equal to c0T and
the economy enjoys full employment. Assume now that the economy
experiences a temporary decrease in the country interest rate followed
by an increase, which causes a boom-bust response in cT. Assume that
in the absence of capital controls, consumption of tradables rises from
c0T to c1T > c0T when the country interest rate falls and then declines back
to c0T once the country interest rate rises. As discussed earlier, in this case
the economy moves from point A to point C during the boom and then
from point C to point D in the bust. During the boom, nominal wages
rise from W0 to W1 > W0 . In the bust, the economy experiences involuntary unemployment in the amount of h 2 hbust because real wages are
stuck at W1 =E0 and downward nominal wage rigidity in combination with
the currency peg prevents real wages from falling to a level consistent
with full employment.
1484
journal of political economy
F IG . 4.—Prudential capital control policy. The figure is drawn under the assumption
that g 5 1.
Consider now the case in which the government implements capital
control taxes in response to the initial interest rate decline and that as a
result of these taxes, the increase in traded consumption is smaller. Specifically, assume that traded consumption now increases from c0T to c2T <
c1T . The demand for nontradables, shown with a broken downwardsloping line in figure 4, shifts up and to the right. As a result nominal
wages increase to W2 and the nontradables supply schedule, shown with
a broken upward-sloping line, shifts up and to the left. The new intersection of the demand and supply schedules is at point C 0 , where the economy enjoys full employment. Because the shift in the demand schedule
in the presence of capital controls is smaller than in their absence, nominal wages rise by less, that is, W2 < W1 . Assume again that when the positive external shock fades away, consumption of tradables falls back to c0T .
The resulting demand schedule is thus the same as the initial one, given
by the solid downward-sloping line in figure 4. The supply schedule (the
upward-sloping broken line) does not shift because as a result of down-
downward nominal wage rigidity
1485
ward nominal wage rigidity, nominal wages cannot decline, that is, wages
remain at W2, and as a result of the currency peg, the exchange rate cannot change, that is, it remains at E 0. The new intersection of the demand
and supply schedules is at point D 0 , where h 2 h cbust workers are involuntarily unemployed. However, the level of unemployment at D 0 is lower
than at D. It follows that by imposing capital controls in response to a
positive external shock, that is to say, by imposing capital controls in a
prudential manner, the government is able to reduce the amount of unemployment that occurs once the positive external shock is over.
But this government intervention comes at the cost of bringing about
an inefficient allocation of traded consumption over time. For capital
controls distort the interest rate perceived by domestic households.
The imposition of capital controls induces households not to take full
advantage of the cheaper cost of borrowing during the boom and not
to reduce their absorption of tradables sufficiently once the interest rate
rises. The figure illustrates the benefits in terms of lower unemployment
that capital controls can bring. But the figure does not capture the costs
in terms of a suboptimal time path of tradable consumption. To analyze
the trade-off between less unemployment and an inefficient allocation
of traded consumption over time, we next characterize Ramsey-optimal
capital control policies more formally.
Assume that the government taxes external debt at the proportional
rate tdt and rebates this source of revenue via a proportional income
y
subsidy denoted tt . The budget constraint of the household is then
given by
ctT 1 pt ctN 1 dt 5 ð1 1 tyt ÞðytT 1 wt ht 1 ft Þ 1
ð1 2 tdt Þdt11
:
1 1 rt
We note again that because all sources of income—ytT , wt ht , and ft—are
taken as exogenous by the household, the income subsidy used to rebate
the revenues from capital controls is nondistorting. The introduction of
a capital control tax changes the household’s first-order condition for
holdings of foreign assets to
lt
1 2 tdt
5 bEt lt11 1 mt :
1 1 rt
(28)
According to this expression, the effective gross interest rate on
debt holdings between periods t and t 1 1 perceived by households is
ð1 1 rt Þ=ð1 2 tdt Þ, which is greater than the gross country interest rate,
1 1 rt, when the government imposes capital controls, that is, when tdt >
0. Observe that the effective interest rate, ð1 1 rt Þ=ð1 2 tdt Þ, like the
country interest rate, 1 1 rt, is in the information set of period t.
1486
journal of political economy
Thus, the capital control policy considered here preserves the statenoncontingent nature of external debt.
The government is assumed to be benevolent and to be endowed with
full commitment. We therefore refer to the government as the Ramsey
planner. We assume that the government pegs the currency and cannot
use labor subsidies of the type studied in Section V. The budget constraint of the government is therefore given by
tyt ðytT 1 wt ht 1 ft Þ 5
tdt dt11
:
1 1 rt
(29)
The policy variable tdt can take positive or negative values. In the former
case it represents a tax on capital inflows and in the latter a subsidy.
Because the monetary authority pegs the currency at all times, equilibrium conditions (17) and (19) become, respectively,
wt ≥ gwt21
(30)
ðwt 2 gwt21 Þ 5 0:
ðht 2 hÞ
(31)
and
We then have the following definition of equilibrium in the economy
with capital controls.
Definition 2 (Equilibrium with capital controls and a currency peg).
Under capital controls and a currency peg, an equilibrium is a set of stoy
chastic processes fctT , ht , wt , dt11 , lt , mt , tt g∞t50 satisfying (10)–(14), (16),
(18), and (28)–(31), given a capital control policy ftdt g∞t50 , initial conditions w21 and d0, and exogenous stochastic processes frt , ytT g∞t50 .
The Ramsey planner’s optimization problem consists in choosing a
tax scheme ftdt g to maximize the household’s lifetime utility function
(1) subject to the equilibrium conditions listed in definition 2. The strategy we follow to characterize the Ramsey allocation is to drop from the
Ramsey planner’s problem all constraints except for (10), (11), (16),
(18), and (30) and then show that the solution to this less constrained
problem satisfies the omitted constraints.
Accordingly, the less constrained Ramsey problem (LCP) is given by
∞
max
fctT ,dt11 ,ht ,wt g
∞
t50
E0 obt U ðAðctT , F ðht ÞÞÞ
t50
subject to (10), (11), (16), (18), and (30), given d0, w21, and the stochastic processes frt , ytT g∞t50 .
We now show that the allocation fctT , dt11 , ht , wt g∞t50 that solves the LCP
satisfies the constraints of the original Ramsey problem listed in definition 2. To see this, use the LCP allocation to construct lt to satisfy (14).
downward nominal wage rigidity
1487
Next, set mt 5 0 for all t.3 It follows that (12) and (13) are satisfied. Now
y
construct tdt to satisfy (28) and tt to satisfy (29). It remains to be shown
that the allocation that solves the LCP satisfies the slackness condition
(31). To see that this is the case, consider the following proof by contradiction. Suppose, contrary to what we wish to show, that the solution to
the LCP implies ht < h and wt > gwt21 at some date t 0 ≥ 0. Consider now a
perturbation to the allocation that solves the LCP consisting in a small
Clearly, this perturbation
increase in hours at time t 0 from ht to h~t ≤ h.
does not violate the resource constraint (10), since hours do not enter
in this equation. From (16) we have that the real wage falls to
0
w
~t ;
0
0
A2 ðctT , F ðh~t ÞÞ 0 ~
F ðht Þ < wt
A1 ðctT , F ðh~t ÞÞ
0
0
0
0
0
0
(recall that the expression in the middle is decreasing in hours). Because A1, A2, and F 0 are continuous functions, expression (30) is satisfied
provided that the increase in hours is sufficiently small. In period t 0 1 1,
restriction (30) is satisfied because w
~ t < wt . We have therefore established that the perturbed allocation satisfies the restrictions of the
LCP. Finally, the perturbation is clearly welfare increasing because it raises
the consumption of nontradables in period t 0 without affecting the consumption of tradables in any period or the consumption of nontradables
in any period other than t 0 . It follows that an allocation that does not satisfy the slackness condition (31) cannot be a solution to the LCP. This
completes the proof that the allocation that solves the LCP is also feasible in the Ramsey planner’s problem. It follows that the allocation that
solves the LCP is indeed the Ramsey-optimal allocation. We summarize
this result in the following proposition.
Proposition 3 (Optimal capital controls under a currency peg). Let
c
, htc , wtc g∞t50 be the allocation associated with the Ramsey-optimal
fctT , dt11
capital control policy in the economy with a currency peg. Then fctT ,
c
, htc , wtc g∞t50 is the solution to the problem of maximizing (1) subject
dt11
to (10), (11), (16), (18), and (30), given d0, w21, and the stochastic processes frt , ytT g∞t50 .
A corollary of this proposition is that one can characterize the Ramsey
allocation as the solution to the following Bellman equation problem:
0
0
c
c
v c ðytT , rt , dt , wt21 Þ 5 max½U ðAðctT , F ðht ÞÞ
T
, rt11 , dt11 , wt Þ
1 bEt v c ðyt11
(32)
3
mt must be chosen to
Note that in states in which the allocation calls for setting dt11 < d,
mt need not be
be zero. However, in states in which the Ramsey allocation yields dt11 5 d,
chosen to be zero. In these states, any positive value of mt could be supported in the decentralization of the Ramsey equilibrium. Of course, in this case, tdt will depend on the chosen
value of mt. In particular, tdt will be strictly decreasing in the arbitrarily chosen value of mt.
1488
journal of political economy
subject to (10), (11), (16), (18), and (30), where v c ðytT , rt , dt , wt21 Þ denotes the value function of the representative household. We exploit this
formulation of the Ramsey problem in our quantitative analysis.
The allocation induced by the Ramsey-optimal capital control policy
can also be supported through consumption taxes. Specifically, assume
that instead of taxing external debt, the government taxes total consumption expenditures, ctT 1 pt ctN , at the rate tct21 , so that the after-tax
cost of consumption in period t is ðctT 1 pt ctN Þð1 1 tct21 Þ. The consumption tax rate is determined one period in advance. That is, in period t
the government announces the tax rate on consumption expenditures
that will be in effect in period t 1 1. One can show that the Ramsey allocation can be supported by a consumption tax process of the form 1 1
tct 5 ð1 2 tdt Þð1 1 tct21 Þ, for any initial condition tc21 > 21, where tdt represents the Ramsey-optimal tax rate on external debt. According to this
expression, if the Ramsey-optimal capital control tax in period t is positive (the planner is discouraging borrowing), then the associated Ramseyoptimal consumption tax scheme stipulates a decline in the consumption
tax rate between periods t and t 1 1 so as to induce households to postpone consumption. Suppose now that the optimal capital control tax is
positive on average, which we will show is the case in the calibrated economy studied in Section IX. Then, it is clear from the above formula that
the associated optimal consumption tax rate converges asymptotically to a
subsidy of 100 percent of consumption expenditure, or tct → 21. This suggests an advantage of capital control taxes over consumption taxes from
a practical point of view.
We also note that the model with Ramsey-optimal capital controls is
equivalent to one in which a benevolent government chooses the level
of external debt and households cannot participate in financial markets
but are hand-to-mouth agents. In this formulation, households receive a
transfer from the government each period and their choice is limited to
the allocation of expenditure between tradable and nontradable goods.
The government then chooses the aggregate level of external debt taking into account the externality created by the combination of downward nominal wage rigidity and a currency peg.
VII.
The Optimality of Prudential Capital Controls
under a Currency Peg: An Analytical Example
In this section, we present an analytical example showing the prudential
nature of optimal capital controls. We characterize the optimal capital
control policy in response to a temporary decline in the interest rate
and show that the Ramsey policy calls for an increase in capital control
taxes while the interest rate is low. This intervention discourages capital
inflows, thereby attenuating the expansion in tradable absorption. The
downward nominal wage rigidity
1489
example highlights the cost of capital controls, which take the form of an
inefficient intertemporal allocation of consumption, and their benefits,
which take the form of lower involuntary unemployment once the boom
is over.
Consider an economy like the one studied thus far in which the government pegs the nominal exchange rate. Assume that preferences are
given by U ðct Þ 5 lnðct Þ and AðctT , ctN Þ 5 ctT ctN . The technology for producing nontradable goods is F ðht Þ 5 hta , with a ∈ (0, 1). Assume that the
economy starts period 0 with no outstanding debt, d0 5 0, that the endowment of tradables, yT, is constant over time, and that the real wage in period 21 equals ayT. Consider a situation in which the economy is subject
to a temporary interest rate decline in period 0. Specifically, suppose
that r0 5 r and rt 5 r > r for t ≠ 0. This interest rate shock is assumed
to be unanticipated. Finally, assume that bð1 1 r Þ 5 1, that g 5 1,
and that h 5 1. The economy is assumed to have been at a fullemployment equilibrium prior to the interest rate shock, with dt 5 0, ctT 5
yT , and ht 5 ctN 5 1 for t < 0.
In online appendix D, we show that under optimal capital controls, all
variables are constant over time starting in period 1. The constancy of all
variables is a consequence of the fact that after period 0 the economy suffers no further disturbances and of the assumptions that b(1 1 r) and g
are both equal to unity. The former parameter restriction ensures the
constancy of tradable consumption and the latter the constancy of the
real wage. This result implies that capital controls are zero starting in period 1. Online appendix D further establishes that in period 0 the
change in tradable consumption is nonnegative, that is, c0T ≥ y T , and
thus capital inflows are nonnegative, that is, d1 ≥ d0 5 0. Intuitively,
the fall in the interest rate encourages international borrowing and consumption. In period 0, the economy enjoys full employment, h0 5 1. This
is natural, since low interest rates stimulate aggregate demand. Finally,
online appendix D shows that starting in period 1, employment is given
by ht 5 c1T =c0T ≤ 1, for t ≥ 1. This expression says that unemployment is
increasing in the contraction in aggregate demand in period 1. Unemployment is persistent because wages cannot fall (g 5 1).
With these results in hand, the Ramsey-optimal capital control problem simplifies to
b
ab
ln c1T 1
ðln c1T 2 ln c0T Þ
max ln c 1
fc ,c ,d g
12b
12b
T
0
T
1
T
0
1
subject to d1 ≥ 0, c0T 5 y T 1 ½d1 =ð1 1 r Þ, and c1T 5 yT 2 ½rd1 =ð1 1 r Þ.
The optimality conditions associated with this problem are the above
three constraints,
1490
journal of political economy
1 1
1
1
11r 1
≤ 0,
2
b
2
ab
1
1 1 r c0T
c1T
c1T r ð1 1 r Þ c0T
(33)
and the slackness condition
8
2
39
< 1 1
=
1
1
1
1
r
1
5 d1 5 0:
2 b T 2 ab4 T 1
T
T
:1 1 r c0
c1
c1
r ð1 1 r Þ c0 ;
The first two terms of optimality condition (33) represent the trade-off
that the representative household would face in an unregulated economy
in deciding whether to take on an additional unit of debt in period 0. An
additional unit of debt allows the household to consume 1=ð1 1 r Þ units
of goods in period 0. In period 1, the household must repay one unit of
consumption to cancel the debt assumed in period 0. We refer to the
first two terms as the private marginal utility of debt. The third term
in (33) captures the externality created by the combination of downward
nominal wage rigidity and a currency peg. It reflects the Ramsey planner’s internalization of the fact that changes in consumption affect unemployment (recall that ht 5 c1T =c0T for all t ≥ 1). This is an equilibrium
effect that is not taken into account by individual consumers. We refer to
the sum of the three terms as the social marginal utility of debt. Since the
third term is negative, we have that the social marginal utility of debt is
always lower than its private counterpart.4
Figure 5 plots the social marginal utility of debt as a function of debt
with a solid line and the private marginal utility of debt with a broken
line. The figure distinguishes two cases, a < r shown in the left panel
and a > r shown in the right panel. It can be shown that when a < r,
the private and social marginal utilities of debt are both downward sloping. The intercept of the private marginal utility of debt is always positive, whereas the intercept of the social marginal utility of debt may be
positive or negative. Recalling that the social marginal utility of debt is
always below its private counterpart, the socially optimal level of debt
(point S in the figure) is always lower than the privately optimal level
of debt (point P in the figure). The Ramsey planner induces this outcome by applying capital controls in period 0. This intervention is prudential in nature because it takes place when the economy is booming.
In this way, the planner ensures that the level of involuntary unemployment that emerges in period 1 (when the boom is over) is lower in the
Ramsey-optimal equilibrium than in the private equilibrium.
4
We thank two anonymous referees for suggesting this interpretation of the optimality
condition of the Ramsey problem.
downward nominal wage rigidity
1491
F IG . 5.—Private and social marginal utility of debt. Color version available as an online
enhancement.
Consider now the case a > r shown in the right panel of figure 5. In this
case the social marginal utility of debt is negative for all nonnegative values of debt. Thus, the socially optimal response to the decline in the interest rate is a corner solution featuring d1 5 0 (point S in the figure).
The Ramsey planner imposes capital controls such that the privately perceived (after-tax) interest rate ð1 1 r Þ=ð1 2 td0 Þ equals 1 1 r.5
Thus, private households have no incentives to alter their consumption plans.6 The benefit of this strong distortion of the intertemporal allocation of tradable absorption is full employment at all times. On the
other hand, the private marginal utility of debt continues to be downward sloping with a positive intercept. As a consequence, the privately
optimal level of debt (point P in the figure) is always positive and thus
higher than the socially optimal level.7
In the case in which a > r, the optimal capital control policy resolves
the trade-off between intertemporal distortions and static distortions entirely in favor of eliminating all static distortions, that is, full employment
5
Implementing the same real allocation via consumption taxes instead of capital controls would require a permanent consumption subsidy at the gross rate ðr 2 r Þ=ð1 1 r Þ
starting in period 1.
6
The change in the world interest rate does not generate a wealth effect because the
desired net asset position prior to the change in the interest rate was nil.
7
The intuition for why a > r is a sufficient condition for the corner solution of no increase in debt in response to a decline in the interest rate is as follows. An increase in debt
implies a fall in employment of at least 1=c0T for all t ≥ 1 (recall that ht 5 c1T =c0T ). This is
equivalent to a decline in nontradable output of a=c0T for all t ≥ 1. The value of this amount
of nontradables in terms of tradables is a since the relative price of nontradables in terms
of tradables is c0T . The present discounted value of a stream of a units of tradables is approximately a/r. Thus, if this value is larger than unity (the increase in tradable consumption afforded by a unit increase in debt in period 0), the planner will never choose to increase debt in period 0.
1492
journal of political economy
at all times. In the case in which a < r, the trade-off is resolved in a more
balanced fashion. The optimal capital control policy consists in reducing
(but not eliminating) inefficient unemployment and distorts (although
less strongly) the intertemporal allocation of consumption. As we will see
shortly, the thrust of these findings carries over to richer economic environments.
VIII. Evidence on Downward Nominal Wage Rigidity
and Estimates of g
The central friction in the present theoretical framework is downward
nominal wage rigidity, embodied in the parameter g. There is abundant
empirical evidence on downward nominal wage rigidity stemming
mostly from developed countries.8 In this section we present novel evidence from emerging countries and propose an empirical strategy for
identifying the wage rigidity parameter g. The strategy consists in observing the behavior of nominal wages during periods of rising unemployment and low inflation. We focus on episodes in which an economy undergoing a severe recession keeps the nominal exchange rate fixed. Two
prominent examples are Argentina during the second half of the Convertibility Plan (1998–2001) and the periphery of Europe during the
Great Recession of 2008.
Figure 6 displays the nominal exchange rate, subemployment (defined as the sum of unemployment and underemployment), nominal
(peso) wages, and real (dollar) wages for Argentina during the period
1996–2006. The subperiod 1998–2001 is of particular interest because
during that time the Argentine central bank was holding on to the currency peg in spite of the fact that the economy was undergoing a severe
contraction and both unemployment and underemployment were in a
steep ascent. In the context of a flexible-wage model, one would expect
that the rise in unemployment would be associated with falling real
wages. With the nominal exchange rate pegged, the fall in real wages
must materialize through nominal wage deflation. However, during this
period, the nominal hourly wage never fell. Indeed, it increased from
7.87 pesos in 1998 to 8.14 pesos in 2001. The present model predicts that
with rising unemployment, the lower bound on nominal wages should
be binding, and therefore, g should equal the gross growth rate of nom8
See, e.g., Gottschalk (2005) for the United States from 1986 to 1993; Barattieri, Basu,
and Gottschalk (2010) for the United States from 1996 to 1999; Daly, Hobijn, and Lucking
(2012) for the United States during the Great Recession of 2008; Eichengreen and Sachs
(1985) for western Europe during the Great Depression of 1929; Holden and Wulfsberg
(2008) for OECD countries; Fortin (1996) for Canada; Kuroda and Yamamoto (2003)
for Japan; and Fehr and Goette (2005) for Switzerland. Kaur (2012) presents evidence
from informal labor markets in rural India.
downward nominal wage rigidity
1493
F IG . 6.—Nominal wages and unemployment in Argentina, 1996–2006. Own calculations
based on nominal exchange rate and nominal wage data from the Bureau of Labor Statistics and subemployment data from Instituto Nacional de Estadistica y Censos de Argentina.
The data are provided with the online materials of this paper.
inal wages. An estimate of the parameter g can then be constructed as
the average quarterly growth rate of nominal wages over the 3-year period considered, that is, g 5 ðW2001 =W1998 Þ1=12 . This yields a value of g of
1.0028.
In order for this estimate of g to represent an appropriate measure of
wage rigidity in the context of the theoretical model, it must be adjusted
to account for the fact that our model abstracts from foreign inflation
and long-run productivity growth. To carry out this adjustment, we use
the growth rate of the US GDP deflator as a proxy for foreign inflation.
Between 1998 and 2001, the US GDP deflator grew by 1.77 percent
per year on average. We set the long-run growth rate in Argentina at
1.07 percent per year, to match the average growth rate of Argentine
per capita real GDP over the period 1900–2005 reported in García-Cicco,
Pancrazi, and Uribe (2010). The adjusted value of g is then given by
1:0028=ð1:0107 1:0177Þ1=4 5 0:9958. This value of g means that real
wages can fall frictionlessly by 1.7 percent per year.
1494
journal of political economy
We note additionally that the fact that Argentine real wages fell significantly and persistently after the devaluation of 2002 (bottom-right
panel of fig. 6) suggests that the 1998–2001 period was one of censored
wage deflation, which further strengthens the view that nominal wages
suffer from downward inflexibility.
Finally, we note that during the 1998–2001 Argentine contraction,
consumer prices, unlike nominal wages, did fall significantly. The consumer price index (CPI) rate of inflation was, on average, 20.86 percent
per year over the period 1998–2001. It follows that real wages rose not
only in dollar terms but also in terms of CPI units. Incidentally, this evidence provides some support for our assumption that downward nominal rigidities are less stringent for product prices than for factor prices.
The second episode from the emerging-market world that we use to
infer the value of g is the Great Recession of 2008 in the periphery of
Europe. Table 1 presents an estimate of g for 12 European economies
that are either on the euro or pegging to the euro. The table shows
the unemployment rate in 2008:Q1 and 2011:Q2. The starting point
of this period corresponds to the beginning of the Great Recession in
Europe according to the Centre for Economic Policy Research Euro Area
Business Cycle Dating Committee. The 2008 crisis caused unemployment
rates to rise sharply across all 12 countries. The table also displays the total growth of nominal hourly labor cost in manufacturing, construction,
and services (including the public sector) over the 13-quarter period
2008:Q1–2011:Q2.9 Despite the large surge in unemployment, nominal
wages grew in most countries, and in those in which they fell, the decline
was modest. The implied value of g, shown in the last column of table 1, is
given by the average growth rate of nominal wages over the period considered, that is, g 5 ðW2011:Q2 =W2008:Q1 Þ1=13 . The estimated values of g range
from 0.996 for Lithuania to 1.028 for Bulgaria.
To adjust g for foreign inflation, we use the fact that over the 13-quarter
sample period considered in table 1, inflation in Germany was 3.6 percent, or about 0.3 percent per quarter. To adjust for long-run growth,
we use the average growth rate of per capita output in the southern periphery of Europe of 1.2 percent per year or 0.3 percent per quarter.10 Allowing for these effects suggests an adjusted estimate of g in the interval
[0.990, 1.022].
Taken together, the evidence examined in this section suggests that
downward nominal wage rigidity is pervasive in emerging countries
and that during low-inflation periods a conservative estimate of g is
9
The public sector is not included for Spain because of data limitations.
This figure corresponds to the average growth rate of per capita real GDP in Greece,
Spain, Portugal, and Italy over the period 1990–2011 according to the World Development
Indicators.
10
downward nominal wage rigidity
1495
TABLE 1
Unemployment, Nominal Wages, and g: Evidence from the Euro Zone
Unemployment Rate
Country
2008:Q1 (%)
2011:Q2 (%)
Wage Growth
W2011:Q2/
W2008:Q2
Bulgaria
Cyprus
Estonia
Greece
Ireland
Italy
Lithuania
Latvia
Portugal
Spain
Slovenia
Slovakia
6.1
3.8
4.1
7.8
4.9
6.4
4.1
6.1
8.3
9.2
4.7
10.2
11.3
6.9
12.8
16.7
14.3
8.2
15.6
16.2
12.5
20.8
7.9
13.3
43.3
10.7
2.5
22.3
.5
10.0
25.1
2.6
1.91
8.0
12.5
13.4
Implied
Value of g
1.028
1.008
1.002
.9982
1.0004
1.007
.996
.9995
1.001
1.006
1.009
1.010
Note.—Own calculations are based on data from Eurostat. The variable
W is an index of nominal average hourly labor cost in manufacturing, construction, and services. Unemployment is the economywide unemployment
rate. The data are provided with the online materials of this paper.
0.99 at a quarterly frequency. This value implies that nominal wages can
decline up to 4 percent per year.
IX. Quantitative Analysis
In this section we characterize quantitatively the behavior of the economy under the alternative policy arrangements analyzed theoretically in
Sections III–VI.
A.
Calibration
We calibrate the model at a quarterly frequency using data from Argentina as shown in table 2. We estimate a bivariate AR(1) process for the
TABLE 2
Baseline Calibration
Parameter
g
j
yT
h
a
y
a
b
Value
Description
.99
Degree of downward nominal wage rigidity
Inverse of intertemporal elasticity of consumption
Steady-state tradable output
Labor endowment
Share of tradables
Elasticity of substitution between tradables and
nontradables
Labor share in nontraded sector
Quarterly subjective discount factor
5
1
1
.26
.44
.75
.9375
1496
journal of political economy
exogenous driving forces ðytT , rt Þ by ordinary least squares using data over
the period 1983:Q1 to 2001:Q4. The empirical measure of ytT is the cyclical component of Argentine GDP in agriculture, forestry, fishing, mining, and manufacturing at 1993 prices. We measure the country-specific
real interest rate as the sum of the Emerging Market Bond Index 1
spread for Argentina and the 90-day US Treasury Bill rate, deflated using
a measure of expected dollar inflation.11 Online appendix E provides
further details on the data sources. The estimated process is
2
3
2
3
T
"
#
ln yt21
ln ytT
0:7901 21:3570
6
7
6
7
4 11r 55
4 1 1 r 5 1 et ;
t
t21
20:0104 0:8638
ln
ln
11r
11r
(34)
"
#!
0:0012346 20:0000776
,
et ∼ N ∅,
20:0000776 0:0000401
and r 5 0.0316. According to these estimates, both ln ytT and rt are highly
volatile, with unconditional standard deviations of 12.2 percent and
1.7 percent per quarter, respectively. The unconditional contemporaneous correlation between ln ytT and rt is high and negative at 20.86, implying that borrowing conditions for debtors tend to deteriorate at the
wrong time, namely, when output is low. The estimated joint autoregressive process implies that both traded output and the real interest
rate are persistent, with first-order autocorrelations of .95 and .93, respectively. The estimated value of the steady-state real interest rate is
high at 3.16 percent per quarter, or 13.2 percent per year.
We set g at 0.99, the lowest of the cross-country estimates reported in
Section VIII. This value imposes the least amount of wage rigidity detected in the Argentine and European data. This value of g means that
nominal wages can fall by up to 4 percent per year. Online appendix G.4
considers the case of g 5 0.98, which allows nominal wages to fall by up
to 8 percent per year.
We assume the constant relative risk aversion form U ðcÞ 5 ðc 12j 2
1Þ=ð1 2 jÞ for the period utility function, the constant elasticity of substitution form
y=ðy21Þ
Aðc T , c N Þ 5 aðc T Þ12ð1=yÞ 1 ð1 2 aÞðc N Þ12ð1=yÞ
for the aggregator function, and the isoelastic form F ðhÞ 5 h a for the
production function of nontradables. Reinhart and Végh (1995) esti11
The country-specific interest rate reflects the fact that, in general, each country borrows at a different interest rate. The country interest rate captures factors such as countryspecific repayment risk. These idiosyncratic interest rate differentials are present even for
countries that are part of a monetary union, such as the members of the euro zone.
downward nominal wage rigidity
1497
mate the intertemporal elasticity of substitution to be 0.21 using Argentine quarterly data. We therefore set j equal to 5. Online appendix G.3
considers a value of j close to 2. We set h equal to unity. Then, if the
steady-state trade balance to output ratio is small, as is the case in Argentina, the parameter a is approximately equal to the share of traded output in total output.12 The share of traded output observed in Argentine
data over the period 1980:Q1–2010:Q1 is 26 percent; hence we set a 5
0.26. Using time-series data for Argentina over the period 1993:Q1–
2001:Q3, González Rozada et al. (2004) estimate the elasticity of substitution between traded and nontraded consumption, y, to be 0.44. This estimate is consistent with the cross-country estimates of Stockman and
Tesar (1995). These authors include in their estimation both developed
and developing countries. Restricting the sample to include only developing countries yields a value of y of 0.43 (see Akinci 2011). Following
Uribe’s (1997) evidence on the size of the labor share in the nontraded
sector in Argentina, we set a equal to 0.75.
We set d at the natural debt limit, which we define as the level of external debt that can be supported with zero tradable consumption when
the household perpetually receives the lowest possible realization of
tradable endowment, yT , and faces the highest possible realization of
the interest rate, r max. Formally, d ; yT ð1 1 r max Þ=r max , which in the present calibration equals 8.34.
Finally, we set b to match an average foreign-debt-to-output ratio of
26 percent per year, a value in line with that reported for Argentina over
our calibration period by Lane and Milesi-Ferretti (2007). The calibrated value of b is small relative to those typically used to calibrate
closed-economy models or open-economy models with a stationarityinducing feature as described in Schmitt-Grohé and Uribe (2003). But
low values of b are more common in open-economy models that do
not include a stationarity-inducing device.
min
min
B. Approximating Equilibrium Dynamics
Here we sketch the numerical solution methods we employ to approximate the equilibrium dynamics under the three policy arrangements we
consider, namely, in ascending order of computational complexity, the
optimal exchange rate policy, a currency peg with optimal capital controls, and a currency peg with free capital mobility.
Under all three policy arrangements, the approximation involves
discretizing the state space. We discretize the exogenous AR(1) process
12
The parameter a is approximately equal to the share of tradable output in total output even though y ≠ 1 because, if the trade balance is near zero, traded output is near
unity, and hours are close to h 5 1, we have that c N 5 yN ≈ c T ≈ yT ≈ 1 and p ≈ ð1 2 aÞ=a,
which implies that y T =ðyT 1 py N Þ ≈ a.
1498
journal of political economy
(34) using 21 equally spaced points for ln ytT in the interval ±0.3858 and
11 equally spaced points for lnð1 1 rt Þ=ð1 1 r Þ in the interval ±0.0539.13
The transition probability matrix of the exogenous driving process is
therefore of size 231 231.14 To compute this matrix, we follow the algorithm described in Schmitt-Grohé and Uribe (2009). The resulting transition probability matrix captures well the covariance matrices of order 0
and 1.
To discretize the endogenous state dt, we use 501 equally spaced points.
We fix the upper bound of the debt grid at 8, which is close to d 5 8:34,
and the lower bound at 25.
When the exchange rate policy takes the form of a currency peg
(whether combined with free capital mobility or with capital controls), a
second endogenous state emerges, namely, past real wages, wt21. We discretize this state using a grid of 500 equally spaced points for the logarithm
of wt21. We set the lowest grid value of wt21 at 0.5 and the highest at 5.3.
The equilibrium dynamics under the optimal exchange rate policy are
obtained from the solution to the value function problem given by the
functional equation (23) and the constraints (8), (10), and (11). We numerically approximate this solution by applying the method of value
function iteration over a discretized state space. Under the optimal exchange rate policy, the state of the economy in period t ≥ 0 is the triplet
fytT , rt , dt g.
The equilibrium dynamics under a currency peg with the optimal capital control policy can be approximated by solving the functional equation (32) subject to (10), (11), (16), (18), and (30). Approximating
the equilibrium dynamics in this environment is more demanding than
doing so under the optimal exchange rate policy because the former
problem includes an additional state variable, namely, wt21. We numerically approximate the equilibrium dynamics by applying the method of
value function iteration over a discretized state space. The state of the
economy in period t ≥ 0 consists of the quadruplet fytT , rt , dt , wt21 g.
The task of approximating the equilibrium dynamics becomes even
more challenging under a currency peg with free capital mobility. As
in the case of a currency peg with optimal capital controls, there are four
state variables, ytT , rt, dt, and wt21. However, under a currency peg with free
capital mobility, aggregate dynamics cannot be cast in terms of a Bellman equation without introducing additional state variables, such as
the individual level of debt, which households perceive as distinct from
its aggregate counterpart. We therefore approximate the solution by
13
able.
The lengths of these intervals are 2 pffiffiffiffiffi
10 times the standard deviation of each vari-
14
Because some pairs ðytT , rt Þ occur with probability zero, the transition probability matrix can be reduced to one of dimension 145 145.
downward nominal wage rigidity
1499
Euler equation iteration over a discretized version of the state space
ðytT , rt , dt , wt21 Þ. Online appendix F describes our numerical algorithm
in more detail. Matlab codes are provided with the online materials of
this paper.
C. Boom-Bust Cycles
We define a boom-bust episode as a situation in which tradable output, ytT ,
is at or below trend in period 0, at least one standard deviation above
trend in period 10, and at least one standard deviation below trend in
period 20. This definition is motivated by the contraction in aggregate
activity observed in Argentina in 2001. We simulate the model economy
for 20 million periods and select all subperiods that satisfy our definition
of a boom-bust episode. We then average across these episodes.
The top two panels of figure 7 display the dynamics of the two exogenous driving forces, tradable output and the country interest rate. Because
our estimate of the exogenous driving forces features a high negative correlation between traded output and the country interest rate, a boom-bust
episode can also be interpreted as one in which the interest rate falls one
standard deviation below mean over a period of 10 quarters and then
rises to one standard deviation above mean in the following 10 quarters.
The middle and bottom panels of the figure depict the model’s predictions during the boom-bust cycle. Solid lines correspond to the economy with a currency peg and free capital mobility, broken lines to the
economy with a currency peg and optimal capital controls, and dotted
lines to the economy with the optimal exchange rate policy.
The middle-left panel of the figure shows that the optimal capital control policy is prudential. Capital controls increase significantly during
the expansionary phase of the cycle, from about 2 percent at the beginning of the episode to 6 percent at the peak of the cycle. During the
contractionary phase of the cycle, capital controls are drastically relaxed.
Indeed at the bottom of the crisis, capital inflows are actually subsidized
at a rate of about 2 percent. The sharp increase in capital controls during
the expansionary phase of the cycle puts sand in the wheels of capital
inflows, thereby restraining the boom in tradable consumption (see
the bottom-right panel). Under a peg with free capital mobility, during
the boom, tradable consumption increases significantly more than under the optimal capital control policy. In the contractionary phase, the
fiscal authority incentivates spending in tradables by subsidizing capital
inflows. As a result consumption falls by much less in the regulated economy than it does in the unregulated one. During the recession, the optimal capital control policy, far from calling for austerity in the form of
severe cuts in tradable consumption, supports this type of expenditure.
That is, the capital control policy stabilizes the absorption of tradable
F IG . 7.—Boom-bust dynamics
downward nominal wage rigidity
1501
goods over the cycle. It follows that the Ramsey-optimal capital control
policy does not belong to the family of beggar-thy-neighbor policies, for
it does not seek to foster trade surpluses during crises.
Because unemployment depends directly on variations in the level of
tradable absorption through the latter’s role as a shifter of the demand
schedule for nontradables and because optimal capital controls stabilize
the absorption of tradables, unemployment is also stable over the boombust cycle. As can be seen from the bottom-left panel of figure 7, in the
peg economy without capital controls, unemployment increases sharply
by over 20 percentage points during the recession. By contrast, under
optimal capital controls, the rate of unemployment rises relatively modestly by about 3 percentage points. It follows that the Ramsey planner’s
trade-off between distorting the intertemporal allocation of tradable
consumption and reducing unemployment is overwhelmingly resolved
in favor of the latter.
Indeed, the rate of unemployment in the peg economy with optimal
capital controls is much closer to the unemployment rate under the optimal exchange rate policy (equal to zero at all times) than to the unemployment rate in the peg economy with free capital mobility. However,
the means by which the policy maker achieves low unemployment in
the peg economy with optimal capital controls and in the optimal exchange rate policy economy are quite different. In the optimal capital
control economy, lower unemployment is the consequence of stabilizing
traded absorption (i.e., stabilizing the demand schedule in fig. 4). By
contrast, under the optimal exchange rate policy, low unemployment
is achieved through a series of large currency devaluations (middle-right
panel of fig. 7) that lower the labor cost in the nontraded sector during
crises (i.e., by shifts in the supply schedule in fig. 4).
D. Level and Volatility Effects of Optimal Capital Controls
Table 3 displays unconditional first and second moments of macroeconomic indicators of interest. On average, the Ramsey planner imposes
a positive tax on external debt of 2.4 percent. This figure implies large
average levels of capital controls, for the effective interest rate faced by
domestic debtors, given by ð1 1 rt Þ=ð1 2 tdt Þ, increases from an average
of 13.2 percent per year under free capital mobility to 24.8 percent
per year under optimal capital controls. The main reason why the Ramsey planner finds it optimal to impose capital controls on average is to
lower the average level of external debt holdings. We postpone an explanation of why this is optimal until Section IX.E.
Table 3 also shows that the tax on debt is highly volatile, with a standard deviation of 5.2 percentage points per quarter. The main payoff
Symbol
Peg with Optimal
Capital Controls
Peg with No
Capital Controls
Optimal
Exchange Rate
Policy
Peg with Optimal
Capital Controls
Peg with No
Capital Controls
Standard Deviation
Capital control rate
Unemployment rate
Consumption
Trade balance
Real wage
Traded output
Interest rate
External debt
Debt-to-output ratio
tdt
0
2.4
0
0
5.2
0
h 2 ht
0
3.1
13.5
0
7.6
11.7
.93
.97
.89
.08
.08
.10
ct
.18
.05
.11
.10
.12
.07
ytT 2 ctT
1.5
2.1
2.3
.8
.6
.7
Wt =Et
1.0
1.0
1.0
.1
.1
.1
ytT
13.2
13.2
13.2
7.4
7.4
7.4
rt
5.8
.9
3.4
.4
2.3
.7
dt
57.9
11.2
26.0
28.6
22.1
12.6
dt =4ðyT 1 pt ctN Þ
Note.—The variables tdt , h 2 ht , and dt =4ðytT 1 pt ctN Þ are expressed in percents; rt is expressed in percent per year; and ct, ytT 2 ctT , Wt =Et , ytT , and dt are
expressed in levels.
Variable
Optimal
Exchange Rate
Policy
Mean
TABLE 3
Optimal Capital Controls: Level and Volatility Effects
downward nominal wage rigidity
1503
of imposing cyclical capital controls is a significant reduction in the average rate of unemployment from 13.5 percent under free capital mobility to 3.1 percent under the optimal capital control policy. This reduction in unemployment is welfare increasing because it raises the average
level of production, and hence also absorption, of nontradables, which
provide utility to domestic households.
The reduction in unemployment is mediated by a significant reduction in the volatility of the growth rate of tradable absorption. The stanT
, not
dard deviation of the growth rate of tradable consumption, ctT =ct21
shown in the table, falls from 5.3 percent under free capital mobility to
2.9 percent under optimal capital controls. The connection between the
volatility of tradable consumption growth and the average level of unemployment follows from the fact that consumption of tradables plays the
role of a shifter of the demand for nontradables (see fig. 3). In turn, the
Ramsey planner succeeds in curbing the variance of tradable expenditure growth by raising the cost of external borrowing during booms
and lowering it during recessions. The correlation between traded output ytT and the capital control rate tdt is .54 and the correlation between
the interest rate rt and tdt is 2.58. Indeed, the Ramsey planner engineers
an effective interest rate that is positively correlated with traded output
in spite of the fact that the interest rate itself is strongly negatively correlated with the latter.
Table 3 shows that the first and second moments of the real (and nominal) wage rates are not significantly affected by the presence of capital
controls. This prediction of the model might appear surprising because
downward wage rigidity is the sole friction in the present model and because unemployment behaves markedly differently in the peg economy
with free capital mobility and the peg economy with optimal capital controls. A reason why the unconditional moments of real wages are little
affected by capital controls is that the lower bound on wages is binding
most of the time in both economies (85 percent of the time under free
capital mobility and 65 percent of the time under optimal capital controls); and when this happens, the wage rate falls at the common gross
rate g. A reason why the first and second moments of unemployment
are so different under free capital mobility and under optimal capital
controls in spite of the similarity in the corresponding moments of real
wages is that when the wage constraint is binding, the magnitude of the
unemployment rate depends on the strength of the domestic absorption
of tradables, which is significantly affected by capital controls.
E. Peg-Induced Overborrowing
Table 3 shows that the average level of external debt in the peg economy
with free capital mobility is more than three times higher than it is in
1504
journal of political economy
the peg economy with optimal capital controls (3.4 vs. 0.9). This prediction of the model is also evident from figure 8, which shows the unconditional distribution of external debt in the economy with a fixed exchange rate and free capital mobility (solid line) and in the economy
with a fixed exchange rate and optimal capital controls (broken line).
The Ramsey planner induces a lower average level of external debt by
taxing borrowing at a positive rate. Recall that the average tax rate on
debt is 2.4 percent per quarter. It follows that the peg economy with free
capital mobility accumulates inefficiently large amounts of external debt
relative to the peg economy with optimal capital controls. In other
words, conditional on being on a fixed exchange rate regime, economies with free capital mobility overborrow.
The reason why the average level of external debt is lower under optimal capital controls than under free capital mobility is that the Ramsey
planner finds it optimal to induce an external debt position that is significantly more volatile than the one associated with free capital mobility.
As shown in table 3, the standard deviation of external debt is 2.3 under
optimal capital controls but only 0.7 under free capital mobility. Similarly, figure 8 shows that the distribution of external debt is significantly
F IG . 8.—The distribution of external debt
downward nominal wage rigidity
1505
more dispersed under optimal capital controls than under free capital
mobility. A more volatile process for external debt requires centering
the debt distribution further away from the natural debt limit for precautionary reasons. In turn, the reason why the Ramsey planner finds wide
swings in the external debt position desirable is that such variations allow
him to insulate the domestic absorption of tradable goods from exogenous disturbances buffeting the economy. Put differently, in the Ramsey
economy, external debt plays the role of shock absorber to a much larger
extent than it does in the economy with free capital mobility.
The purpose of optimal capital controls is not to close the current account. On the contrary, under optimal capital controls, the economy
makes more heavy use of the current account to smooth consumption
than it does under free capital mobility. To see this, note that the current
account is given by the change in net external debt and that, as is apparent from figure 8, the net external debt has a much more dispersed distribution under optimal capital controls than under free capital mobility.
Figure 8 shows that the distribution of net external debt under the optimal exchange rate policy (dotted line) has a higher mean and is much
less dispersed than under a currency peg with optimal capital controls.
This difference highlights the fact that the two policies achieve reductions in unemployment (relative to a currency peg with free capital mobility) through very different means. Under the optimal exchange rate
policy, the government eliminates unemployment via devaluations that
shift the supply of nontradables to offset variations in the demand for
nontradables brought about by fluctuations in the desired consumption
of tradables. In this way, the policy maker achieves two goals, full employment and an efficient allocation of tradable consumption over time. Under a currency peg with optimal capital controls, the policy maker cannot induce shifts in the supply of nontradables, since its hands are
tied by the currency peg and the presence of downward nominal wage
rigidity. Instead, the government reduces unemployment by minimizing
shifts in the demand for nontradables. To this end, the government
levies capital controls to stabilize the desired demand for tradable consumption, which is the key shifter of the demand schedule for nontradables. In turn, as explained above, a smooth path for tradable consumption can be supported only by large swings in the country’s
external debt position, which by necessity must be centered further away
from the natural debt limit than it would be if tradable consumption
were allocated optimally.
Finally, it is of interest to point out that the optimal capital control policy characterized here is complementary to the one that emerges in
models of overborrowing due to collateral constraints (e.g., Korinek
2010; Bianchi 2011). In this class of models, households’ ability to borrow is increasing in the value of output in terms of tradables. In turn,
1506
journal of political economy
the value of output in terms of tradables is increasing in the relative price
of nontradables. This relative price is endogenous to the model but exogenous to the household, which creates a pecuniary externality. The
government understands that in equilibrium the relative price of nontradables is increasing in the absorption of tradables. Consequently, to
induce a more relaxed collateral constraint on average, the government
implements a policy that raises the average consumption of traded
goods. To support higher average consumption of tradables, the economy must hold a lower average stock of external debt. This is achieved
through capital controls. Thus, this literature shares two characteristics
with the present model, namely, an externality that leads to overborrowing and positive average capital controls as a second-best remedy.
The key difference, of course, resides in the nature of the externality, financial frictions in one case and downward wage rigidity in the other.
F. Welfare Costs of Free Capital Mobility under a Currency Peg
We have established that in the peg economy, free capital mobility entails excessive external debt and unemployment. Both of these factors
tend to depress consumption and therefore reduce welfare. In this section, we quantify the welfare losses associated with free capital mobility
in economies subject to a currency peg.
Define the welfare cost of a currency peg under free capital mobility
conditional on state st ; fytT , rt , dt , wt21 g, denoted lf ðst Þ, as the percentage increase in the lifetime consumption stream required by an individual living in the economy with a currency peg and free capital mobility in
state st to be as well off as an individual living in an economy with the optimal exchange rate policy. Formally, lf ðst Þ solves
(
)
f
∞
l
ðs
Þ
f
t
11
E obj U ct1j
st 5 v o ðytT , rt , dt Þ,
100
j50
f
where ct denotes consumption in the economy with a peg and free capital mobility and, as defined earlier, v o ðytT , rt , dt Þ denotes the value function in the economy with the optimal exchange rate policy in state
ðytT , rt , dt Þ. Because the state vector st is stochastic, the conditional welfare
cost measure, lf ðst Þ, is itself stochastic. We report the mean of lf ðst Þ over
the distribution of st in the peg economy with free capital mobility. Formally, let pf ðst Þ denote the unconditional probability of st under a peg
with free capital mobility. Then
lf 5
op ðs Þl ðs Þ:
f
f
t
st
t
(35)
downward nominal wage rigidity
1507
Similarly, the welfare cost of a currency peg under the optimal capital
control policy conditional on state st, denoted lc ðst Þ, is defined as the
permanent percentage increase in the lifetime consumption stream required by an individual living in the economy with a currency peg and
optimal capital controls in state st to be as well off as an individual living
in the economy with the optimal exchange rate policy. That is, lc ðst Þ is
implicitly given by
(
)
∞
lc ðst Þ
j
c
E ob U ct1j 1 1
st 5 v o ðytT , rt , dt Þ,
100
j50
where ctc denotes consumption in the economy with a peg and optimal
capital controls. Letting pc ðst Þ denote the unconditional probability of
st under a peg with optimal capital controls, we have that the expected
value of the welfare cost of a peg under the optimal capital control policy
is given by
lc 5
op ðs Þl ðs Þ:
c
c
t
t
(36)
st
Recalling that the optimal exchange rate policy achieves the Paretooptimal allocation, one can interpret lf as the distance, in welfare terms,
between the first-best allocation and the allocation induced by a currency
peg with free capital mobility. Similarly, lc can be interpreted as the distance between the first-best allocation and the one induced by a currency
peg coupled with Ramsey-optimal capital controls.
Table 4 shows that the average welfare costs of free capital mobility for
a pegging economy are large. The representative household living in the
economy with free capital mobility requires, on average, an increase of
11.6 percent in consumption every period to be indifferent between living under a peg with free capital mobility and living in an economy with
the optimal exchange rate policy.
The optimal capital control policy greatly reduces the pains of currency pegs. Households living in an economy with a currency peg and optimal capital controls require a 3.7 percent increase in consumption each
period to be as well off as living in the economy with the optimal exchange
rate policy. The welfare gain of moving from a peg, with or without optimal capital controls, to the optimal exchange rate policy has three components: One is a reduction in unemployment, which translates into higher
production and consumption of nontradables. This benefit is larger for
the peg economy with free capital mobility. The second component is related to transitional dynamics along which households liquidate precautionary savings through higher-than-average consumption of tradables.
This effect can be seen from figure 8, showing that the average level of external debt is higher under the optimal exchange rate policy than under
11.6
10.1
17.6
8.4
6.2
19.0
9.3
2.1
3.7
5.0
6.0
.6
.4
.8
.6
.3
Peg with Optimal
Capital Controls
lc
13.5
7.8
15.3
12.4
9.5
33.5
33.5
33.5
3.1
1.9
3.7
.5
.4
1.3
1.8
8.4
Peg with Optimal
Capital Controls
100 E½1 2 ðht =hÞ
Peg with No
Capital Controls
Unemployment Rate
Note.—Welfare costs are relative to the optimal exchange rate policy (or first-best allocation) and are expressed in percent of consumption per period
(see expressions [35] and [36]). Unemployment rates are expressed in percent. For details see online app. G.
1. Baseline
2. Production in traded sector
3. Greece
4. j 5 1/y 5 2.27 and b 5 .962
a. Less wage rigidity (g 5 .98)
b. Endogenous labor supply (d 5 .5)
c. Endogenous labor supply (d 5 .75)
d. Endogenous labor supply (d 5 1)
Economy
Peg with No
Capital Controls
lf
Welfare Cost
TABLE 4
The Costs of Currency Pegs
downward nominal wage rigidity
1509
either of the two peg arrangements. The reduction in savings is greater for
the peg economy with optimal capital controls. The third component is a
lower long-run level of tradable consumption under the optimal exchange rate policy. This component represents a cost and is higher under optimal capital controls than under free capital mobility. Overall, the
welfare gains are dominated by the reduction in unemployment.
A relevant question from a policy perspective is what are the welfare
gains for a pegging economy with free capital mobility to adopt optimal
capital controls. One might be tempted to conclude that the answer is
lf 2 lc , or 7.9 percent of consumption per period. But this computation
would fail to correctly take into account the transitional debt dynamics
involved in moving from free capital mobility to optimal capital controls.
As can be seen from figure 8, moving from a peg economy with free capital mobility to a peg with optimal capital controls requires reducing the
average level of external debt. This deleveraging is costly, since it implies a temporarily lower-than-average level of consumption of tradables.
This sacrifice is painful by itself, but it also causes unemployment to be
higher along the transition (recall that consumption of tradables is a
shifter of the demand for nontradables). In the long run the economy
with optimal capital controls will enjoy a higher average level of tradable
consumption than the economy with free capital mobility. In sum, moving from free capital mobility to optimal capital controls has the benefits
of lower long-run unemployment (13.5 vs. 3.1 percent), higher long-run
consumption of tradables (6.9 percent higher), but a transitional cost associated with debt deleveraging. Of course, by definition, there must be
net gains from moving from free capital mobility to optimal capital controls. In our economy these gains turn out to be 2.2 percent of consumption per period.15 This is a large number as welfare costs go in business
cycle analysis but is not as high as the naive measure lf 2 lc .
Our finding of large welfare costs of currency pegs (with or without
capital controls) stands in stark contrast to a large body of work, pioneered by Lucas (1987), suggesting that the costs of business cycles
(not just of suboptimal monetary policy) are small. Lucas’s approach
to computing the welfare costs of business cycles abstracts from two
features that are central determinants of welfare costs in our model,
15
Formally, the welfare gain of switching from a peg with free capital mobility to a peg
with optimal capital controls, denoted lf → c ðst Þ, is given by
lf → c 5
op ðs Þl
f
t
f →c
ðst Þ,
st
where lf → c ðst Þ is implicitly given by
)
(
(
)
∞
∞
lf → c ðst Þ
j
f
j
c
E ob U ct1j 1 1
st 5 E ob U ðct1j Þ st :
100
j50
j50
1510
journal of political economy
namely, the effect of volatility on mean unemployment and transitional
dynamics. The lack of connection between volatility and means within
Lucas’s approach can be seen by noticing that it consists in first removing a trend from a consumption time series and then evaluating a
second-order approximation of welfare using observed deviations of
consumption from trend. Under this approach, the welfare cost of business cycles depends only on the volatility of the cyclical component of
consumption. Implicit in this methodology is the assumption that the
trend is unaffected by policy. In our model, however, suboptimal monetary policy creates an endogenous connection between the amplitude of
the business cycle and the average rate of unemployment. In turn,
through its effect on the average level of unemployment, suboptimal exchange rate policy has a significant effect on the average level of consumption of nontradables (recall that nontradables are produced with
labor). It follows that applying Lucas’s methodology to data stemming
from our model would overlook the effects of policy on mean consumption and therefore would result in spuriously low welfare costs.
The importance of transitional dynamics for welfare can be seen by
comparing the mean and standard deviation of consumption in the
economy with a peg and optimal capital controls and the economy with
optimal exchange rate policy. The welfare cost of pegs with optimal
capital controls relative to the optimal exchange rate policy is 3.7 percent of consumption per period even though consumption under the
former policy has a higher mean (0.97 vs. 0.93) and the same volatility
(0.08) as under the latter. The reason why the peg with optimal capital
controls is welfare dominated by the economy with the optimal exchange rate policy is that the former is associated with an inefficiently
low level of external debt. As a result, an economy that switches from a
peg with optimal capital controls to the optimal exchange rate policy
enjoys a transition with high absorption of tradables as it accumulates
external debt.
Because our model is stylized, we interpret the present welfare evaluation as suggestive. The sensitivity analysis presented in online appendix
G and summarized in table 4 provides some more support for the size of
the welfare losses reported here. In particular, it shows that the main
findings are robust to allowing for production in the traded sector, estimating the driving process using data from Greece, considering a higher
intertemporal elasticity of substitution (or lower value of j), allowing for
more wage flexibility, and introducing endogenous labor supply.
X. Conclusion
We document the presence of downward nominal wage rigidity in lowinflation emerging economies with fixed nominal exchange rates. We
downward nominal wage rigidity
1511
estimate that even in the context of massive unemployment, nominal
hourly wages fail to fall at a rate larger than 1 percent per quarter. With
this motivation in mind, we develop a dynamic stochastic model of an
open economy with downward nominal wage rigidity and analyze its adjustment to large external shocks.
A key insight of the model is that the combination of downward nominal wage rigidity and a fixed exchange rate gives rise to a negative externality. The nature of the externality is that private absorption expands
too much in response to favorable shocks, causing inefficiently large increases in real wages. No problems are manifested in this phase of the
cycle. However, as the economy falls back to its trend path, wages fail
to decline quickly enough because they are downwardly rigid. In addition, the central bank, having its hands tied by the commitment to a
fixed exchange rate, cannot deflate the real value of wages via a devaluation. In turn, high real wages and a contracting level of aggregate absorption cause involuntary unemployment. Individual agents are conscious of this mechanism but are too small to internalize it. The
externality thus leads to overborrowing during booms and to excessive
unemployment during downturns.
We show that without policy intervention, currency pegs can be painful
for economies that are subject to large external shocks. For example, a calibrated version of our model predicts that an external shock, defined as a
two standard deviation collapse in the terms of trade and a two standard
deviation increase in the country interest rate, causes an increase in unemployment of more than 20 percent of the labor force. This figure is consistent with the unemployment rates observed in the aftermath of recent
large contractions in emerging-market economies that followed a fixed exchange rate regime, including Argentina 1998–2001 and the periphery of
the European Union after 2008.
One policy option to address the unemployment problem is to abandon
the currency peg in favor of the optimal exchange rate policy. We show that
the optimal exchange rate policy calls for large devaluations in response to
large external shocks. These devaluations reduce the real value of wages,
allowing the labor market to clear. In the calibrated model, boom-bust cycles of the type observed in Argentina in 1998–2001 and in the periphery of
Europe after 2008 call for devaluations of about 100 percent.
We demonstrate that an alternative to devaluation is the optimal fiscal
policy. For example, optimal wage subsidies at the firm level financed by
income taxes at the household level can fully undo the distortions created by the combination of downward nominal wage rigidity and a currency peg and therefore can bring about the Pareto-optimal allocation.
We argue, however, that such policies might not be practical to implement in a political environment focused on fiscal austerity such as the
one prevailing in Europe after 2008. This motivates our analysis of opti-
1512
journal of political economy
mal capital control policy, broadly interpreted as regulations of crossborder financial flows, as an alternative way to address the aforementioned negative externality.
We show that the optimal capital control policy is prudential in nature.
The benevolent government taxes capital inflows in good times and subsidizes external borrowing in bad times. The key role of capital controls
is to insulate the domestic absorption of tradable goods from external
shocks. In this way, the government avoids that external disturbances
spill over to the nontraded sector causing unemployment. Capital controls, although they represent only a second-best policy, can go a long
way toward restoring full employment in fixed exchange rate economies.
Under our baseline calibration, the average rate of unemployment falls
from 13.5 to 3.1 percent when the currency peg is coupled with optimal
capital controls.
These results suggest that when labor markets suffer from downward
nominal wage rigidity and the exchange rate is fixed, countercyclical
capital controls can be an effective instrument for macroeconomic stabilization.
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